User blog:Lord Aspect/Infinities
Infinitiy is a number (or not) that has no end. Infinity means Not Finite, so, Infinity is actually not finite. Lord Aspect defined some tiers of Infinity. Tier 1 Tier 1 Infinity is a start of all infinities. First infinity is N0 (Aleph Null) aka ω (Omega). Technically, some numbers are literally after it, despite all infinites are meant to be equal (long to explain). Tiers from 2 till ω These tiers are calculated from the value of number, that this tier represents. T = IN№ - ω + 1, where IN№ is a infinity, we need to classify, and T is tier number. Examples: *ω + 1 (Tier 2) *ω + 10 (Tier 11) Tiers from ω till ω^2 These tiers can be calculated by another formula, native to previous. For first, you have to dissolve a number into a set of similliar numbers multiplying. For example: 3ω = ω + ω + ω. After that, use already coined formula. Examples: *2ω (Tier ω + 1) *3ω (Tier 2ω + 1) *10ω (Tier 9ω + 1) ω-Exponential Tiers aka Tiers from ω^2 till ε0 ω-Exponential Tiers are tiers, which could get coined by raising ω to higher power. To calculate tier of ω-Exponential Numbers, you will have to dissolve formulas like a^n to this: a * (for n times in total) * a. After that, use previously learned dissolvance of numbers. But this system is considered to be useless, because result is incalculable. So, Lord Aspect created the Second-Order Infinity (SecTiers). ScT = n - 1, where ScT is SecTier, and n is taken from equation a^n = IN№, with a = ω Examples: *ω^2 (SecTier 1) *ω^10 (SecTier 9) *ω^(ω+1) (SecTier ω) To calculate furthrer numbers, we have to use another system of calculating tiers. Let's imagine we have an infinite number: ω^ω^ω. ScT (ω^ω^ω) = ω^ω - 1. Numbers are getting incomputable again. So, we have to use new formula (again) and a new tier system (again). Third-Order Infinity (TriTiers) Tiers can be calculated by using this formula: TrT = m - 1, where TrT is TriTier, and m is taken from equation a^n^m, with a = ω. Examples: *ω^ω^14 (TriTier 13) *ω^ω^(ω+1) (TriTier ω) Heck! We need new system again! All of those systems are reccurring until ω-Order Infinity (InfTier). Formula is: ωT = x - 1, where ωT is InfTier, and x is taken from equation a^... (ω times in total) ...^x, and a = ω Example: *ε0 = ω^.... (ω times in total) ....^ω (InfTier ω) Now we have to convert all of this into something more understandable. Now, tier is writen like this: INTn here: INT = infinity tier; n = tier number Examples: *ω^(ω+1) (Tier ω2) *ε0 (Tier ωω) Untierable There are specific numbers that are untierable. Their tiers cannot be calculated. Inaccessible (θ) In set theory, an uncountable cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic. Compact (ח‬) Unfoldable (ך) Ultimately Incalculable (ψ) Ultimatum Examples: *CAI (Ω) *Sigma (Σ) Category:Blog posts